The two-dimensional hydrogen atom revisited

The bound state energy eigenvalues for the two-dimensional Kepler problem are found to be degenerate. This "accidental" degeneracy is due to the existence of a two-dimensional analogue of the quantum-mechanical Runge-Lenz vector. Reformulating the problem in momentum space leads to an integral form of the Schroedinger equation. This equation is solved by projecting the two-dimensional momentum space onto the surface of a three-dimensional sphere. The eigenfunctions are then expanded in terms of spherical harmonics, and this leads to an integral relation in terms of special functions which has not previously been tabulated. The dynamical symmetry of the problem is also considered, and it is shown that the two components of the Runge-Lenz vector in real space correspond to the generators of infinitesimal rotations about the respective coordinate axes in momentum space.Comment: 10 pages, no figures, RevTex

Instability of (1+1) de sitter space in the presence of interacting fields

Instabilities of two dimensional (1+1) de Sitter space induced by interacting fields are studied. As for the case of flat Minkowski space, several interacting fermion models can be translated into free boson ones and vice versa. It is found that interacting fermion theories do not lead to any instabilities, while the interacting bosonic sine-Gordon model does lead to a breakdown of de Sitter symmetry and to the vanishing of the vacuum expectation value of the S matrix.Comment: 7 page

Final State Interaction Phases in B→Kπ B \to K \pi Decay Amplitudes

A simple Regge pole model for $K\pi$ scattering explains the large $e^{i \delta}$ between isospin amplitudes which is observed at the D meson mass ($\delta \approx \pi/2$). It predicts $\delta \approx 14^{\circ}- 20^{\circ}$ at the B mass. Implications for ($B \to K \pi$) decays and extensions of the model to other two-body decay channels are briefly discussed.Comment: 8pages,late

Quark resonances and high E_t jets

Possible spin-3/2 quark resonances would have a significant effect on high E_{\mbox{\rm t}} jet production through their contribution to the subprocess $q+{\bar q}\rightarrow g+g$. Such enhancements are compared to a, recently reported, anomaly in inclusive jet production at the CDF detector.Comment: 7 pages set in RevTex with four postscript figures appended- all uuencode

Conjugate field and fluctuation-dissipation relation for the dynamic phase transition in the two-dimensional kinetic Ising model

The two-dimensional kinetic Ising model, when exposed to an oscillating applied magnetic field, has been shown to exhibit a nonequilibrium, second-order dynamic phase transition (DPT), whose order parameter Q is the period-averaged magnetization. It has been established that this DPT falls in the same universality class as the equilibrium phase transition in the two-dimensional Ising model in zero applied field. Here we study for the first time the scaling of the dynamic order parameter with respect to a nonzero, period-averaged, magnetic `bias' field, H_b, for a DPT produced by a square-wave applied field. We find evidence that the scaling exponent, \delta_d, of H_b at the critical period of the DPT is equal to the exponent for the critical isotherm, \delta_e, in the equilibrium Ising model. This implies that H_b is a significant component of the field conjugate to Q. A finite-size scaling analysis of the dynamic order parameter above the critical period provides further support for this result. We also demonstrate numerically that, for a range of periods and values of H_b in the critical region, a fluctuation-dissipation relation (FDR), with an effective temperature T_{eff}(T, P, H_0) depending on the period, and possibly the temperature and field amplitude, holds for the variables Q and H_b. This FDR justifies the use of the scaled variance of Q as a proxy for the nonequilibrium susceptibility, \partial / \partial H_b, in the critical region.Comment: revised version; 31 pages, 12 figures; accepted by Phys. Rev.

QCD Factorization for B→ππB\to\pi\pi Decays: Strong Phases and CP Violation in the Heavy Quark Limit

We show that, in the heavy quark limit, the hadronic matrix elements that enter $B$ meson decays into two light mesons can be computed from first principles, including `non-factorizable' strong interaction corrections, and expressed in terms of form factors and meson light-cone distribution amplitudes. The conventional factorization result follows in the limit when both power corrections in $1/m_b$ and radiative corrections in $\alpha_s$ are neglected. We compute the order-$\alpha_s$ corrections to the decays $B_d\to\pi^+\pi^-$, $B_d\to\pi^0\pi^0$ and $B^+\to\pi^+\pi^0$ in the heavy quark limit and briefly discuss the phenomenological implications for the branching ratios, strong phases and CP violation.Comment: 6 pages, 1 figur

Bloch Brane

We investigate a system described by two real scalar fields coupled with gravity in (4, 1) dimensions in warped spacetime involving one extra dimension. The results show that the parameter which controls the way the two scalar fields interact induces the appearence of thick brane which engenders internal structure, driving the energy density to localize inside the brane in a very specific way.Comment: 13 pages, 6 figures; some misprints corrected, to appear in JHE

Desperately Seeking Non-Standard Phases via Direct CP Violation in b→sg∗b\to sg^\ast Process

Attributing the recent CLEO discovery of $B \to \eta' + X_s$ to originate (primarily) from the fragmentation of an off-shell gluon ($g^*$) via $b \to s + g^*$, $g^* \to g + \eta'$, we emphasize that many such states ($X_g$) should materialize. Indeed the hadronic fragments ($X_g$) of $g^*$ states are closely related to those seen in $\psi \to \gamma (\phi, \omega) + X_g$. A particular final state of considerable interest is $X_g=K^+K^-$. Signals from such states in $B$ decays can be combined to provide a very sensitive search for CP violating phase(s) from non-standard physics. The method should work even if the contribution of these source(s) to the rates is rather small ($\sim10$) to the point that a comparison between theory and experiment may find it extremely difficult to reveal the presence of such a new physics.Comment: 16 pages, 5 figure

Anomalous Chromomagnetic Moments of Quarks and Large Transverse Energy Jets

We consider the jet cross sections for gluons coupling to quarks with an anomalous chromomagnetic moment. We then apply this to the deviation and bounds from QCD found in the CDF and D0 Fermilab data, respectively, to find a range of possible values for the anomalous moments. The quadratic and quartic terms in the anomalous moments can fit to the rise of a deviation with transverse energy. Since previous analyses have been done on the top quark total cross section, here we assume the same moment on all quarks except the top and find the range $|\kappa'| \equiv |\kappa/(2 m_q)| = 1.0\pm 0.3$ TeV$^{-1}$ for the CDF data. Assuming the anomalous moment is present only on a charm or bottom quark which is pair produced results in a range $|\kappa'_{b,c}| = 3.5 \pm 1.0$ TeV$^{-1}$. The magnitudes here are compared with anomalous magnetic moments that could account for $R_b$ and found to be in the same general range, as well as not inconsistent with LEP and SLD bounds on $\Delta \Gamma_{\text{had}}$.Comment: REVTeX, 11 pages, 2 postscript figure

Lorentz and Galilei Invariance on Lattices

We show that the algebraic aspects of Lie symmetries and generalized symmetries in nonrelativistic and relativistic quantum mechanics can be preserved in linear lattice theories. The mathematical tool for symmetry preserving discretizations on regular lattices is the umbral calculus.Comment: 5 page